Reminder: Coins are not ‘stored’ in wallets. A wallet is more akin to a keychain, with coins always living on the blockchain itself

This means if you import a private key into a new wallet, you are not ‘moving’ the coins from one wallet to another – you are making a copy of that key for that new ‘keychain’ (wallet). The coins will be accessible from both wallets at once.

If you don’t want to do this, you can sometimes ‘sweep’ the coins from one wallet into another. This is like having a new key cut and changing the lock.

This is quite a fundamental mechanism of crypto wallets, but is quite a common misunderstanding – one I had myself until fairly recently!